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Many real-world phenomena, in particular in economics, are modelled as constrained optimization problems. The usefulness of such models depends on the values of their parameters garbage in, garbage out. Traditional statistical methods generally lack the ability to make efficient use of the multiple data sources upon which such models depend and to provide estimates that are consistent with a model structure that may be both non-linear and inequality-constrained. This is book proposes and demonstrates methods for econometric specification of parameters of constrained optimization models, with special attention to issues that arise when (i) inequality constraints are involved and/or (ii) when the estimation problem is ill-posed (underdetermined) or data come from diverse sources. The general approach followed here is to directly estimate the optimality conditions of the optimization model, together with additional equations for including prior information. The book blends theoretical analyses with didactic as well as full-scale empirical applications, and should prove useful to applied modellers in various areas.